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Displacement and Position Sensors (Part 1)

Written by George Novacek

Measurement Techniques

Object tracking is a required feature in many modern control systems. In this article, George examines measurement techniques used generate electrical output with respect to distance or position.

Without displacement and position sensors, robotics and position control systems couldn’t exist. In this article, I’ll cover measurement techniques generating electrical output with respect to distance or position. The terminology encountered in the literature on this subject is not very consistent, so to avoid confusion, I use the term displacement sensors to refer to devices that continuously track an object’s movement. Position sensors are those that indicate when a target object has reached its destination. Displacement sensors can be divided into three major categories: linear, rotary, and contactless. Once again, an ambiguity exists in literature as to what constitutes a contactless sensor.


Some refer to Linear Variable Differential Transformers (LVDT) as contactless, as opposed to, for instance, potentiometers, whose wiper and thus circuit is attached to the measured object. For clarity, I shall call sensors contactless if and only if none of their parts are mechanically coupled with the measured object, such as in radar or ultrasonic ranging.

LVDTs have been around for about a century. With their unlimited resolution while working in the harshest environments, including space, they have been the undeclared kings of displacement sensors. Figure 1 depicts an LVDT. The primary coil is excited by an AC signal. The core of the LVDT is attached to the object whose movement is to be tracked. As the core moves, the inductive coupling between the primary and the secondary windings changes, which in turn changes the output voltages of the secondary windings.

Figure 1  This is a simplified cross-section of an LVDT. Coils are often tapered or otherwise formed to ensure the best linearity.
Figure 1
This is a simplified cross-section of an LVDT. Coils are often tapered or otherwise formed to ensure the best linearity.
Figure 2 Here are two common electrical interfaces of LVDTs and RVDTs: direct (a) and ratiometric (b).
Figure 2
Here are two common electrical interfaces of LVDTs and RVDTs: direct (a) and ratiometric (b).

There are two common interfaces for variable differential transformers (VDTs). These are shown in Figure 2. Originally, the topology in Figure 2a had been widely used. The secondary windings are connected to generate voltages in opposite phase. With the core at null, both secondary voltages are identical, 180° out of phase. Consequently, the VDT output is zero. Moving the core increases the output of one winding while decreasing the other, with the phase indicating the direction of the movement. This configuration has a major drawback in that it is sensitive to the variations of the excitation voltage as well as its frequency. This disadvantage is eliminated by the ratiometric configuration supported by integrated circuits (e.g., Analog Device AD598) also containing an integral excitation generator. Figure 2b explains the decoding principle.

Presently VA and VB are often digitized and the displacement calculated by software. My tests showed that for an LVDT designed for 3-V/3.2-kHz excitation the ratiometric output remained consistent through its entire displacement range with the excitation ranging from 2 to 4.5 VRMS and frequencies 2,000 to 4,000 Hz.

Besides LVDTs, there are principally identical Rotary Variable Differential Transformers (RVDT). An RVDT’s construction resembles that of an electric motor with the armature designed to provide linear output. RVDT electrical interface is the same as for the LVDT. The VDTs are also available as autotransformers to reduce their cost and weight. Their interface requires only three wires.


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LVDTs are built to measure displacement from about 0.02” (0.508 mm) to 20” (508 mm). I saw one LVDT with the maximum stroke of 40” (1,016 mm). RVDTs can achieve linearity up to about ±80°. VDTs are not inexpensive. For use in harsh operating environments, such as aerospace, with stringent characteristics, they may cost more than $1,000.

Where low cost is crucial and the environment permits it, displacement can be measured by potentiometers. Linear potentiometers with the wiper attached to the moving object are available with typically 100 mm (3.94”) stroke and 5-to10-kΩ resistance. Care must be taken to provide stable excitation voltage and to avoid electrically loading the output to minimize error. A high-impedance buffer amplifier will do the job and reduce electromagnetic interference (EMI) susceptibility of the interface.

It is often advantageous to convert linear displacement into a rotary one and then use a rotary potentiometer (preferably multiturn), an RVDT, or a rotary encoder as the transducer. A mechanical transmission—even as simple as a cord wound on the shaft of the sensor to rotate it—significantly increases its linear displacement range.

Rotary displacement is frequently measured by optical or magnetic encoders. These are absolute or incremental, both with their particular advantages and disadvantages. Figure 3 illustrates a simple 3-bit absolute encoder. The black segments stand for “1” and the white ones for “0.” They are usually read by optical means. The practically achievable resolution is up to about 22 bits. These sensors are light, work reliably in the harshest environments, and retain their position information even after losing power.

Incremental encoders, generally optically or magnetically (e.g., with Hall sensors) read, detect a rotating wheel’s number of revolutions or teeth. An approximately 24-bit resolution can be achieved. Quadrature output, using two sensors, is needed to indicate the movement’s direction. Figure 4 illustrates how it is done.

Incremental sensors have to be “homed” to a reference position before they can be successfully used. You can observe such initial homing with scanners, printers, plotters, and so forth.

Figure 3  This is a three-bit absolute encoder.
Figure 3
This is a three-bit absolute encoder.
Figure 4 Generating quadrature output from an incremental encoder
Figure 4
Generating quadrature output from an incremental encoder
Figure 5 The principle of magnetostrictive sensors
Figure 5
The principle of magnetostrictive sensors

Magnetostrictive sensors feature greater range than LVDTs, from about 0.1” (2.54 mm) to 780” (20 m), excellent accuracy and linearity. Unfortunately, they do not work very well at high temperatures and can be pricey.

The principle of their operation lies in the magnetostrictive properties of ferromagnetic materials such as iron, nickel, or cobalt. When a wire made of such a material is exposed to a magnetizing force H, its dimensions will change, as Figure 5 shows. This mechanical response of ferromagnetic materials to a magnetizing force, called the Villari effect, is due to the randomly arranged collection of permanent magnets, called domains, inside the material. Upon magnetization the domains align with their axes approximately parallel to each other. This also works the other way around. Applying a mechanical force to such a material changes its magnetic properties.

When a current flows through the magnetostrictive wire and an axial magnetic field is applied to it, the wire twists at the location of the field—a so-called Wiedemann effect. A 1-to-2-µs current pulse applied to the wire causes the momentary twist, which travels through the wire as an ultrasonic wave at a speed of approximately 3,000 m/s.


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To measure displacement, a permanent magnet is attached to the measured object. A current pulse is applied to the wire and the time for the waveguide twist to arrive is measured. From this time the location, that is the distance of the magnet, can be calculated.


Strain gauges and capacitive sensors are used for small displacements such as we may find in weight scales, aircraft landing gear (i.e., to measure total weight before the takeoff), and so forth. The strain gauge is a strip of a metal wire, a foil, or a semiconductor material placed on a piece of an adhesive-backed plastic, not dissimilar to a postage stamp, attached to the measured object. Strain resulting from changes in the length or any deformation of the material changes the gauge’s resistance applied to it. Linear strain is defined as the ratio of the change in length divided by the original length of the measured object The change ∆R of the ohmic resistance (R) of the gauge enables us to calculate the displacement:

G is the gauge factor. Typically, G = 2 for metal wires or foil, G = +100 for a P-type semiconductor, and G = –100 for an N-type semiconductor. e is the strain’s value. L is the length of the measured object. ∆L its change in length.

Displacement is also measured by capacitive sensors, although their inherent nonlinearity limits their useable range. The capacitance of two parallel plates is defined by:

Figure 6 describes the principle of the capacitive sensing. The capacitance of the sensor can be changed three different ways. By moving the plates closer or farther apart modifies d in the equation. Or, the overlap of the two electrodes can be changed, thus modifying the capacitor area A. And, finally, insertion of a dielectric material between the two plates (e.g., a plastic rod) will modify the dielectric constant er.

Figure 6 The principle of capacitive displacement sensing.
Figure 6
The principle of capacitive displacement sensing.

Position sensing refers to the generation of an electrical signal when an object reaches its destination. This is to confirm the object’s location, to prevent system overdrive and so forth. A good example is an electric garage door opening system with two position sensors responsible for turning the motor off at desired positions.

Unfortunately, I am out of space. I’ll visit the topics of contactless displacement sensors and position sensors in Part 2 of this series. 

Read Part 2 Here

Analog Devices, “LVDT Signal Conditioning Circuit,” CN-0288, 2014.
G. Novacek, “Accurate Linear Measurement,” Circuit Cellar 106, 1999.

AD598 LVDT Signal conditioner
Analog Devices |


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George Novacek was a retired president of an aerospace company. He was a professional engineer with degrees in Automation and Cybernetics. George’s dissertation project was a design of a portable ECG (electrocardiograph) with wireless interface. George has contributed articles to Circuit Cellar since 1999, penning over 120 articles over the years. George passed away in January 2019. But we are grateful to be able to share with you several articles he left with us to be published.

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Displacement and Position Sensors (Part 1)

by George Novacek time to read: 6 min